2022/07/19 by Hong, Jiuzu, Kumar, Shrawan · 1 citation
#14D21 #14H60 #14H81 #17B67 #17B68 #17B81 #81R10 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2207.09578
Let Γ be a finite group acting on a simple Lie algebra \mathfrakg and acting on a s-pointed projective curve (Σ, p=\p1, …, ps\) faithfully (for s≥ 1). Also, let an integrable highest weight module \mathscrHc(λi) of an appropriate twisted affine Lie algebra determined by the ramification at pi with a fixed central charge c is attached to each pi. We prove that the space of twisted conformal blocks attached to this data is isomorphic to the space associated to a quotient group of Γ acting on \mathfrakg by diagram automorphisms and acting on a quotient of Σ. Under some mild conditions on ramification types, we prove that calculating the dimension of twisted conformal blocks can be reduced to the situation when Γ acts on \mathfrakg by diagram automorphisms and covers of ℙ1 with 3 marked points. Assuming a twisted analogue of Teleman's vanishing theorem of Lie algebra homology, we derive an analogue of the Kac-Walton formula and the Verlinde formula for general Γ-curves (with mild restrictions on ramification types). In particular, if the Lie algebra \mathfrakg is not of type D4, there are no restrictions on ramification types.